eye won't mirror over correctly?
I hate to tell you this but the Mirror Modifier is grossly ignorant of the 3D Cursor up to the point of complete and perpetual denial. 

It mirrors either around the object origin of the object it's assigned to or it takes the orientation and location of the mirror object if you configure it that way. Your screenshot makes it hard to see where the OO of the eyeball is, but I guess it's not on the centerline.

My guess: it's directly beneath the line created by the two eyeballs intersecting.

https://docs.blender.org/manual/en/dev/modeling/modifiers/generate/mirror.html

So you can either put the eyeball (its origin, not the mesh) in the middle of your head and then, in Edit Mode, move it to the side or you can keep the eyeball's object origin in its center and use either the character's OO or an empty for mirroring or you can put your 3D Cursor in the middle, select the eyeball and use 'set origin to 3d cursor' in the tools.